02 Introduction To Economics: December 2008

Wednesday, December 17, 2008

Partial Specialization & Trade Pissing Me Off

I understand how to combine the 2 constraints to make one graph, but then trying to figure out the rest is frustrating and pissing me off. It's so much easier when they go the full specialization route for the trade :( Anyways if anybody has a clearer explanation let me know, and based on all the readings and the Unit Information Sheet I uploaded earlier, they're gonna want the Neo-Classical Economic models and trade and specialization based on the partial specialization parameters!!!!!! Oh well, perhaps I don't understand because I speak American not English LOL

Definitions

a) axiom or premise - a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
b) empirical - Verifiable or provable by means of observation or experiment
c) positive statement - What is, a fact
normative statement - What should be
d) Fundamental economic problem - How to fulfill unlimited needs & wants with scarce resources
e) Economic good - tangible goods/products
f) PPF - or “transformation curve” is a graph that shows the different rates of production of two goods that an economy (or agent) could efficiently produce with limited productive resources. Points along the curve describe the trade-off between the two goods, that is, the opportunity cost. Opportunity cost here measures how much an additional unit of one good costs in units forgone of the other good. The curve illustrates that increasing production of one good reduces maximum production of the other good as resources are transferred away from the other good.
g) a binding constraint - When we want one or more of one commodities in our bundle, we have to give up some of the other commodities.
h) productive efficiency - when production is along the PPF curve
i) opportunity cost - The cost of an alternative that must be forgone in order to pursue a certain action. Put another way, the benefits you could have received by taking an alternative action.
j) Marginal Opportunity Cost - aka marginal rate of transformation (MRT). It describes numerically the rate at which one good can be transformed into the other. It is also called the (marginal) "opportunity cost” of a commodity, that is, it is the opportunity cost of X in terms of Y at the margin. It measures how much of good Y is given up for one more unit of good X or vice versa. The shape of PPF is commonly drawn as concave downward to represent increasing opportunity cost with increased output of a good. Thus, MRT increases in absolute size as one moves from the top left of the PPF to the bottom right of the PPF.
k) Autarky - the condition of self-sufficiency, esp. economic, as applied to a nation.

Mathematical Appendix: The calculus of marginals and totals

In the text we considered several functions. When some variable Y is a function of another variable X, we can write

Y = f(X). (A1)

For every given value of Y, this function gives us a corresponding value of X. The marginal value of Y is the rate at which Y is tending to change as X changes. Mathematically, this is the derivative of Y with respect to X. We can write

Marginal value of Y = dY/dX, (A2)

or, in two other common alternative notations,

Marginal value of Y = f'(X),

Marginal value of Y = f_x.

If we have only the marginal relationship in (A2), we can derive the relationship of total Y to total X in (A1) up to an arbitrary constant by integrating the marginal function:

Y = ∫f'(X)dX + C, (A3)

where C is the constant of integration.

Consider an example. Let the function be a quadratic:

Y = a + bX + cX², c <>a, b. (A4)

The graph of this relationship will show Y rising up to some maximum value and then falling as X increases further.

The marginal value of Y is

dY/dX = b + 2cX. (A5)

Since c <>b when X is zero. This tells us that the increment to Y is positive as X increased from 0 but falls steadily and eventually becomes negative. Where the marginal value is positive the graph of the original relationship is positively sloped, and where it is negative the graph of the original line is negatively sloped.

Letting the values of the parameters be a = 10, b = 2 and c = -0.1, we have

Y = 10 + 2X - 0.1X². (A6)

The marginal value of Y is then given by

dY/dX = 2 - 0.2X,

which is zero at X = 10, positive for smaller X, and negative for larger X. This shows that increments to X up to 10 cause Y to increase while they cause Y to decrease when X exceeds 10.

If all we knew was the marginal revenue relationship of equation (A5), we could determine the total value of Y as

Y = ∫(2 - 0.2X)dX = 2X - 0.1X² + C. (A7)

Since the original constant of a = 10 in equation (A4) disappears on differentiation, integration can only put back an arbitrary constant, C. In other words, there is no way we can discover the value of the original constant, a. But we can find the equation of the relationship between X and Y and know its shape except for an arbitrary parameter that shifts points on it upwards or downwards by a constant amount.